The Bulldogs (4-7, 3-3 WAC) scored the game's first 17 points, then allowed 21 straight by the Warriors (5-6, 3-4) before scoring the game-winning touchdown early in the fourth quarter to snap a three-game losing skid.
Carr completed 19 of 29 attempts with no interceptions. Robbie Rouse rushed for a season-high 176 yards for Fresno State, which scored on its first three drives.
The Warriors took the lead with 6:28 remaining in the third quarter on David Graves' 69-yard touchdown pass to Billy Ray Stutzmann.
Two plays into the fourth quarter, Carr hooked up with Josh Harper on a 43-yard scoring strike that proved to be the game winner. Harper beat the cornerback on the post route and Carr's pass was just out of the reach of the leaping safety.